Algebraic lattice codes for linear fading channels

TL;DR

This paper explores the use of algebraic lattice codes for linear fading channels, building on classical lattice theory to approach channel capacity with codes that have linearly growing Hermite invariants.

Contribution

It introduces algebraic lattice code constructions tailored for linear fading channels, extending classical lattice sphere packing results to fading environments.

Findings

Lattice codes with linearly growing Hermite invariants achieve a constant gap to capacity in fading channels.

Theoretical connections between lattice geometry and channel capacity are established for fading scenarios.

The approach generalizes classical AWGN results to more complex channel models.

Abstract

In the decades following Shannon's work, the quest to design codes for the additive white Gaussian noise (AWGN) channel led to the development of a rich theory, revealing a number of beautiful connections between information theory and geometry of numbers. One of the most striking examples is the connection between classical lattice sphere packing and the capacity of the AWGN channel. The main result states that any family of lattice codes with linearly growing Hermite invariant achieves a constant gap to capacity. These classical results and many more can be found in the comprehensive book by Conway and Sloane [5].....